Least Squares Sinusoidal Parameter Estimation

There are many ways to define ``optimal'' in signal modeling. Perhaps
the most elementary case is *least squares estimation*. Every
estimator tries to measure one or more parameters of some underlying
*signal model*. In the case of sinusoidal parameter estimation,
the simplest model consists of a single complex sinusoidal component
in additive white noise:

where is the complex amplitude of the sinusoid, and is white noise (defined in §C.3). Given measurements of , , we wish to estimate the parameters of this sinusoid. In the method of least squares, we minimize the sum of squared errors between the data and our model. That is, we minimize

with respect to the parameter vector

(6.34) |

where denotes our signal model:

(6.35) |

Note that the error signal is

- Sinusoidal Amplitude Estimation
- Sinusoidal Amplitude and Phase Estimation
- Sinusoidal Frequency Estimation

[How to cite this work] [Order a printed hardcopy] [Comment on this page via email]

Copyright ©

Center for Computer Research in Music and Acoustics (CCRMA), Stanford University